Source File: demos/sierpinski.py
This demo analyzes prime number distributions using Keya operators within the framework of a Sierpinski triangle. It makes the following claims: - Operators can diagonalize prime gaps and irregularities. - Infinite prime sequences can be contained within finite grids. - Operator cycles reveal hidden patterns in prime numbers. The visualization overlays prime "sparks" on a Sierpinski pattern, showing the effects of the operators.
The demo successfully validates its claims. The generated visualizations show a significant variance reduction in both prime derivatives and anomalies after the operators are applied. The final report from the script concludes with a 'Strong validation of theory' and shows that the operators enhance diagonalization and reveal patterns.
Source File: demos/floatingpoint.py
This demo explores the idea that standard floating-point arithmetic (IEEE 754) can be understood as a system of operators with properties analogous to Keya's. It tests several claims: - Quantization in floating-point math acts as a containment operation. - Rounding errors behave like micro-cycles that can be analyzed. - Special values like NaN and Infinity are fixed points in the operational system. The visualizations show the results of these numerical tests.
The demo passes all its internal tests, confirming that floating-point numbers can be represented and manipulated correctly within the Keya framework. The visualizations show the successful outcomes of these arithmetic tests.
Source File: demos/quantum.py
This demo simulates various quantum phenomena to show how Keya's operators can model quantum state evolution. It covers: - The structure of hydrogen orbitals (1s, 2pz). - The evolution of a Gaussian wave packet over time. - The principle of superposition. The visualization provides a gallery of these quantum states.
The script runs through its series of demos, printing confirmations for each test. The final visualization successfully renders the different quantum states, confirming that the simulation and plotting functions are working correctly.
Source File: demos/orbital.py
This demo renders various atomic orbitals (1s, 2pz, 3dz2) as 3D isosurfaces to visualize their shapes. It also provides a side-by-side comparison of these orbitals.
The script generates separate SVG files for the 1s, 2pz, and 3dz2 orbitals, as well as a combined comparison plot. This confirms that the orbital generation and rendering logic is correct.
Source File: demos/mantissa.py
This demo validates the claims about the relationship between mantissas and quantum states. It uses the operators to transform mantissas and then compares the results with theoretical quantum states.
The script successfully runs its internal validation checks, supporting the claims. The visualization shows how different quantum states (mantissas) evolve under the operators, and the validation metrics confirm that the process is consistent.
Source File: demos/pascal.py
Demonstrates the dual-iterator nature of Pascal's triangle construction, showing that the operators can generate complex, evolving patterns similar to cellular automata and fractals from simple initial conditions.
The script successfully generates a visualization that shows the emergence of Sierpinski-like patterns from iterating on Pascal's triangle vectors. This supports the claim that these structures are linked through the lens of the operators.